In the graphs in Fig. 3-6, where y replaces f(x) as the dependent variable in functions, as is common in graphing, indicate which graphs are graphs of functions and which are not.

From the definition of a function, we know that for each value of x, there can be one and only one value of y. If, for any value of x in the domain, therefore, a vertical line can be drawn which intersects the graph at more than one point, the graph is not the graph of a function. Applying this criterion, which is known as the vertical line test, we see that (a), (c), and

(d) are functions; (b), (e)

and

(f) are not.

Transcribed Image Text:

y y (a) (d) x x y y (b) (c) x S x